For classical ML, we implement property prediction with classical shadows based on random Clifford measurements 
[1]}. The sample complexity to
predict \(M\)  Pauli observables up to small constant accuracy is known to be \(\mathcal {O}(\max _{x} \operatorname{tr}(P_x^2) \log (M))\) . Using \(\operatorname{tr}(P_x^2)=\operatorname{tr}(I^{\otimes n})=2^n\)  and \(M=4^n\) , this upper bound simplifies to \(\mathcal {O}(n 2^n)\) . The numerical experiments confirm this theoretical prediction.
